Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
798 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 211 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23773960 | C2 | semidirect |
| 3. #23763034 | C2 | semidirect |
| 4. #23763029 | C2 | semidirect |
| 5. #23763023 | C2 | semidirect |
| 6. C2×#19098284 | C2 | semidirect |
| 7. C79×#3160 | C2 | semidirect |
| 75. C2×C8×C79 | SD16 | semidirect |
| 122. #3160 | D79 | semidirect |
| 128. C79 | #19608 | semidirect |
| 194. C2×C8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773960 | 2 |
| #23773828 | 2 |
| #23763034 | 2 |
| #23763029 | 2 |
| #23763023 | 2 |
| C2×#19098284 | 2 |
| C79×#3160 | 2 |
| #19608 | 79 |